Differentiation...

$$A$$ is twice as fast as $$B$$ is thrice as fast as $$C$$. The journey covered by $$C$$ in $$42$$ minutes, what will be covered by $$A$$ is 

Find $$\dfrac{dy}{dx}$$ of function $$y= e^{x^3} +\dfrac{1}{2} \log x $$

If $$^{n + 1}{C_3} = 4\,{\,^n}{C_2}$$ then $$n=$$

$$x^{\frac{1}{2}} + 1=  t$$
differentiate w.r.t. x

If the letter of the word $$LATE$$ be permuted and the words so formed be arranged as in a dictionary . Then the rank of $$LATE$$ is :

Differentiate: $$x^{100} + \sin x - 1$$

Choose the most appropriate option which fits this pattern

Solve:$$\dfrac{2}{2}+\dfrac{3}{3}+\dfrac{4}{4}+$$...... + upto $$1000$$ terms= ?

$$3$$ letters are posted in $$5$$ letters boxes. If all the letters are not posted in the same box, then number of ways of posting is

There are $$10$$ trees between two stations $$A$$ and $$B$$. Three of them are to be cut down then the total number of ways so that no two trees are to be cut consecutively, is